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inn [45]
3 years ago
5

Someone please explain step by step.

Mathematics
1 answer:
dolphi86 [110]3 years ago
6 0

Answer:

{10}^{th}  \: term  =  \frac{5}{512}

Step-by-step explanation:

geometric progression formula:

{n}^{th} \:  term  = ar ^{n - 1}

given:

common ratio, r = 1/2

first \: term \:  = 5

1) find the value of a

{n}^{th}  \: term \:  = a {r}^{n - 1}

we're finding the 1st term, so substitute 1 into n:

{1}^{st}  \: term  = a( \frac{1}{2} ) {}^{1 - 1}

first term is 5. so we substitute 5 into the equation:

5 = a(1)

a = 5

2) find the 10th term

we're finding the 10th term, so substitute 10 into the equation and don't forget to substitute 5 into a:

{10}^{th}  \: term  = 5( \frac{1}{2} ) {}^{10 - 1}

{10}^{th}  \: term  = 5( \frac{1}{512} )

{10}^{th}  \: term =  \frac{5}{512}

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